Level set representations are the most common choice for the implementation of variational frameworks in computer vision since they are implicit, intrinsic, parameter and topology free.
A use of level set representations to deal with computer vision related problems has increased within the computer vision community. Prior art techniques based on these methods and used in the computer vision application domain are wide and not restricted to image segmentation, restoration, impainting, tracking, shape from shading, three dimensional reconstruction, and medical image segmentation.
Level set methods have been exhaustively studied and are also applied to other scientific domains, such as, geometry, robotics, fluids, and semiconductor design. Many of the application domains share a common concern, that is, tracking moving interfaces. Level set representations are computational methods that are well suited to perform the task of tracking moving surfaces. Level set representations can be used in any dimension, for example, curves, surfaces, and hyper-surfaces, and are parameter free. Level set representations can change, naturally, the topology of an evolving interface. Moreover, level set representations provide a natural way to determine and estimate geometric properties of an evolving interface.
Level set representation techniques are well suited to deal with non-rigid objects and motions, since the techniques refer to local characteristics and can deform an interface pixel-wise. When solid/rigid motions and objects are considered, the techniques exhibit a limited performance as compared to parametric methods that can capture a rigid/solid objects structure well. This difference is due to the fact that local propagation is very sensitive and fails to take full advantage of well determined physical constraints, such as, solid shape models. It is clear, that evolving interfaces are powerful tools when using level set representations, that have certain strengths and some limitations. For example, the property of locality is not helpful when a considered task refers to the extraction of solid objects; however, the property of locality is a vital element when a considered task refers to non-rigid motions and objects.
Visual space comprises objects from both categories. For example, most active human organs cannot be considered solid, but at the same time, forms of active human organs are well constrained within a family of shapes that cannot be fully characterized using parametric models. The use of level set based methods are suitable for this type of application due to their ability to deal with local deformations. Moreover, the use of shape prior knowledge is a valuable element that can further improve the performance of these methods.
Therefore, a need exists for the ability to constrain level set representations to follow a shape global consistency while preserving the ability to capture local deformations.